Equivalent viscous damping for a system with energy dissipation via elastic instabilities

This paper presents a study to investigate the equivalent viscous damping (EVD) for the hysteretic response of a multiple cosine-curved dome (MCCD) system. The system comprises of several serially connected units with elastic multistable behavior. The system relies on consecutive snap-through buckling events of the connected units to elastically dissipate energy. The study aims to facilitate the direct displacement-based design of structures incorporating such systems as the main damping mechanism to dissipate seismic energy. Time-history analyses of linear and nonlinear single degree of freedom systems were performed to compare spectral displacements and EVD ratios of the hysteretic response of MCCD systems to their substitute linear systems in terms of maximum displacements. A set of 62 ground motion records were considered for the analysis. A statistical study was conducted on the resulting displacements and the EVD ratios to develop expressions for EVD ratios of the hysteretic response. Results show that using proposed EVD ratios for the substitute linear systems yields good approximations for the peak spectral displacements compared to the original nonlinear systems.